Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7056,2,Mod(1567,7056)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7056, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7056.1567");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7056.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(56.3424436662\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 2352) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.7 | ||
Root | \(-1.60021 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7056.1567 |
Dual form | 7056.2.b.w.1567.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7056\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1765\) | \(4609\) | \(6175\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.21486i | 1.43773i | 0.695151 | + | 0.718864i | \(0.255338\pi\) | ||||
−0.695151 | + | 0.718864i | \(0.744662\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.36710i | 0.412195i | 0.978531 | + | 0.206098i | \(0.0660765\pi\) | ||||
−0.978531 | + | 0.206098i | \(0.933924\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.93015i | 0.812678i | 0.913722 | + | 0.406339i | \(0.133195\pi\) | ||||
−0.913722 | + | 0.406339i | \(0.866805\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.91037i | 1.67601i | 0.545661 | + | 0.838006i | \(0.316279\pi\) | ||||
−0.545661 | + | 0.838006i | \(0.683721\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.35449 | −1.68724 | −0.843618 | − | 0.536943i | \(-0.819579\pi\) | ||||
−0.843618 | + | 0.536943i | \(0.819579\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.62774i | 0.756436i | 0.925717 | + | 0.378218i | \(0.123463\pi\) | ||||
−0.925717 | + | 0.378218i | \(0.876537\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.33530 | −1.06706 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.11185 | 0.206466 | 0.103233 | − | 0.994657i | \(-0.467081\pi\) | ||||
0.103233 | + | 0.994657i | \(0.467081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.70319 | −1.56314 | −0.781569 | − | 0.623819i | \(-0.785580\pi\) | ||||
−0.781569 | + | 0.623819i | \(0.785580\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.63792 | 1.25567 | 0.627833 | − | 0.778348i | \(-0.283942\pi\) | ||||
0.627833 | + | 0.778348i | \(0.283942\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 0.833147i | − 0.130116i | −0.997881 | − | 0.0650579i | \(-0.979277\pi\) | ||||
0.997881 | − | 0.0650579i | \(-0.0207232\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.82362i | 0.735595i | 0.929906 | + | 0.367797i | \(0.119888\pi\) | ||||
−0.929906 | + | 0.367797i | \(0.880112\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.95367 | 0.430837 | 0.215418 | − | 0.976522i | \(-0.430888\pi\) | ||||
0.215418 | + | 0.976522i | \(0.430888\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.57794 | 0.628829 | 0.314414 | − | 0.949286i | \(-0.398192\pi\) | ||||
0.314414 | + | 0.949286i | \(0.398192\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.39502 | −0.592625 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.0985 | −1.83546 | −0.917732 | − | 0.397200i | \(-0.869982\pi\) | ||||
−0.917732 | + | 0.397200i | \(0.869982\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 11.0618i | − 1.41632i | −0.706052 | − | 0.708160i | \(-0.749525\pi\) | ||||
0.706052 | − | 0.708160i | \(-0.250475\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.42002 | −1.16841 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 12.1545i | − 1.48490i | −0.669900 | − | 0.742452i | \(-0.733663\pi\) | ||||
0.669900 | − | 0.742452i | \(-0.266337\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 12.6249i | − 1.49830i | −0.662402 | − | 0.749148i | \(-0.730463\pi\) | ||||
0.662402 | − | 0.749148i | \(-0.269537\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.49011i | 0.759610i | 0.925067 | + | 0.379805i | \(0.124009\pi\) | ||||
−0.925067 | + | 0.379805i | \(0.875991\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.79367i | 0.876856i | 0.898766 | + | 0.438428i | \(0.144465\pi\) | ||||
−0.898766 | + | 0.438428i | \(0.855535\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.87502 | 0.974159 | 0.487080 | − | 0.873358i | \(-0.338062\pi\) | ||||
0.487080 | + | 0.873358i | \(0.338062\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.2159 | −2.40965 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.6146i | 1.33715i | 0.743646 | + | 0.668574i | \(0.233095\pi\) | ||||
−0.743646 | + | 0.668574i | \(0.766905\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 23.6436i | − 2.42579i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 13.8811i | − 1.40942i | −0.709497 | − | 0.704708i | \(-0.751078\pi\) | ||||
0.709497 | − | 0.704708i | \(-0.248922\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.65891i | − 0.165068i | −0.996588 | − | 0.0825338i | \(-0.973699\pi\) | ||||
0.996588 | − | 0.0825338i | \(-0.0263013\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.30791 | −0.128872 | −0.0644359 | − | 0.997922i | \(-0.520525\pi\) | ||||
−0.0644359 | + | 0.997922i | \(0.520525\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.15204i | 0.691414i | 0.938343 | + | 0.345707i | \(0.112361\pi\) | ||||
−0.938343 | + | 0.345707i | \(0.887639\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.0443 | −1.44098 | −0.720491 | − | 0.693464i | \(-0.756083\pi\) | ||||
−0.720491 | + | 0.693464i | \(0.756083\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.4530 | 1.45369 | 0.726846 | − | 0.686800i | \(-0.240985\pi\) | ||||
0.726846 | + | 0.686800i | \(0.240985\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.6627 | −1.08755 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.13104 | 0.830095 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.07795i | − 0.0964149i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.16478i | 0.192094i | 0.995377 | + | 0.0960468i | \(0.0306198\pi\) | ||||
−0.995377 | + | 0.0960468i | \(0.969380\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.97877 | −0.434997 | −0.217499 | − | 0.976061i | \(-0.569790\pi\) | ||||
−0.217499 | + | 0.976061i | \(0.569790\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.68980 | 0.315241 | 0.157620 | − | 0.987500i | \(-0.449618\pi\) | ||||
0.157620 | + | 0.987500i | \(0.449618\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0577 | 1.02272 | 0.511360 | − | 0.859367i | \(-0.329142\pi\) | ||||
0.511360 | + | 0.859367i | \(0.329142\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.00580 | −0.334982 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.57445i | 0.296842i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.30262 | −0.270561 | −0.135280 | − | 0.990807i | \(-0.543194\pi\) | ||||
−0.135280 | + | 0.990807i | \(0.543194\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.9511i | 1.54222i | 0.636701 | + | 0.771111i | \(0.280299\pi\) | ||||
−0.636701 | + | 0.771111i | \(0.719701\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 27.9795i | − 2.24737i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 0.886436i | − 0.0707453i | −0.999374 | − | 0.0353726i | \(-0.988738\pi\) | ||||
0.999374 | − | 0.0353726i | \(-0.0112618\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 19.3538i | − 1.51591i | −0.652310 | − | 0.757953i | \(-0.726200\pi\) | ||||
0.652310 | − | 0.757953i | \(-0.273800\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 25.4855 | 1.97213 | 0.986065 | − | 0.166360i | \(-0.0532014\pi\) | ||||
0.986065 | + | 0.166360i | \(0.0532014\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.41421 | 0.339555 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.6924i | 1.64925i | 0.565683 | + | 0.824623i | \(0.308613\pi\) | ||||
−0.565683 | + | 0.824623i | \(0.691387\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.2824i | 0.918032i | 0.888428 | + | 0.459016i | \(0.151798\pi\) | ||||
−0.888428 | + | 0.459016i | \(0.848202\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 2.74444i | − 0.203993i | −0.994785 | − | 0.101996i | \(-0.967477\pi\) | ||||
0.994785 | − | 0.101996i | \(-0.0325230\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.5548i | 1.80531i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.44716 | −0.690844 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 22.8857i | − 1.65595i | −0.560766 | − | 0.827974i | \(-0.689493\pi\) | ||||
0.560766 | − | 0.827974i | \(-0.310507\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.6163 | 1.05211 | 0.526053 | − | 0.850452i | \(-0.323671\pi\) | ||||
0.526053 | + | 0.850452i | \(0.323671\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.5430 | −1.74861 | −0.874307 | − | 0.485374i | \(-0.838684\pi\) | ||||
−0.874307 | + | 0.485374i | \(0.838684\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.04659 | −0.428631 | −0.214316 | − | 0.976764i | \(-0.568752\pi\) | ||||
−0.214316 | + | 0.976764i | \(0.568752\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.67845 | 0.187071 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 10.0543i | − 0.695471i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 9.33513i | − 0.642657i | −0.946968 | − | 0.321328i | \(-0.895871\pi\) | ||||
0.946968 | − | 0.321328i | \(-0.104129\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.5072 | −1.05758 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.2484 | −1.36206 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.48794 | 0.367500 | 0.183750 | − | 0.982973i | \(-0.441176\pi\) | ||||
0.183750 | + | 0.982973i | \(0.441176\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.03813 | 0.0689028 | 0.0344514 | − | 0.999406i | \(-0.489032\pi\) | ||||
0.0344514 | + | 0.999406i | \(0.489032\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 15.6039i | − 1.03113i | −0.856850 | − | 0.515566i | \(-0.827582\pi\) | ||||
0.856850 | − | 0.515566i | \(-0.172418\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.21561 | −0.603734 | −0.301867 | − | 0.953350i | \(-0.597610\pi\) | ||||
−0.301867 | + | 0.953350i | \(0.597610\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.49562i | 0.619426i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.54809i | 0.100137i | 0.998746 | + | 0.0500687i | \(0.0159440\pi\) | ||||
−0.998746 | + | 0.0500687i | \(0.984056\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 3.68527i | − 0.237389i | −0.992931 | − | 0.118695i | \(-0.962129\pi\) | ||||
0.992931 | − | 0.118695i | \(-0.0378709\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 21.5498i | − 1.37118i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.1940 | −1.65335 | −0.826676 | − | 0.562679i | \(-0.809771\pi\) | ||||
−0.826676 | + | 0.562679i | \(0.809771\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.95947 | −0.311799 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.833147i | 0.0519703i | 0.999662 | + | 0.0259851i | \(0.00827226\pi\) | ||||
−0.999662 | + | 0.0259851i | \(0.991728\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.04212i | 0.310911i | 0.987843 | + | 0.155455i | \(0.0496845\pi\) | ||||
−0.987843 | + | 0.155455i | \(0.950316\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.7174i | 0.904085i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.85594i | 0.296072i | 0.988982 | + | 0.148036i | \(0.0472951\pi\) | ||||
−0.988982 | + | 0.148036i | \(0.952705\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.2488 | −1.35152 | −0.675759 | − | 0.737122i | \(-0.736184\pi\) | ||||
−0.675759 | + | 0.737122i | \(0.736184\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 7.29388i | − 0.439837i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.670606 | 0.0402928 | 0.0201464 | − | 0.999797i | \(-0.493587\pi\) | ||||
0.0201464 | + | 0.999797i | \(0.493587\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.5971 | −1.52700 | −0.763499 | − | 0.645810i | \(-0.776520\pi\) | ||||
−0.763499 | + | 0.645810i | \(0.776520\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.1115 | 0.660510 | 0.330255 | − | 0.943892i | \(-0.392865\pi\) | ||||
0.330255 | + | 0.943892i | \(0.392865\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −30.7533 | −1.80902 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 19.2818i | − 1.12645i | −0.826303 | − | 0.563226i | \(-0.809560\pi\) | ||||
0.826303 | − | 0.563226i | \(-0.190440\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 45.3245i | − 2.63890i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.6298 | −0.614738 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 35.5622 | 2.03628 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.0058 | 1.48423 | 0.742115 | − | 0.670273i | \(-0.233823\pi\) | ||||
0.742115 | + | 0.670273i | \(0.233823\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.0772 | −1.08177 | −0.540885 | − | 0.841096i | \(-0.681911\pi\) | ||||
−0.540885 | + | 0.841096i | \(0.681911\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.3583i | 1.20724i | 0.797272 | + | 0.603620i | \(0.206276\pi\) | ||||
−0.797272 | + | 0.603620i | \(0.793724\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.74131 | −0.434795 | −0.217398 | − | 0.976083i | \(-0.569757\pi\) | ||||
−0.217398 | + | 0.976083i | \(0.569757\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.52001i | 0.0851043i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 50.8223i | − 2.82783i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 15.6332i | − 0.867176i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.675988i | 0.0371557i | 0.999827 | + | 0.0185778i | \(0.00591385\pi\) | ||||
−0.999827 | + | 0.0185778i | \(0.994086\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 39.0748 | 2.13489 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.176755 | −0.00962847 | −0.00481423 | − | 0.999988i | \(-0.501532\pi\) | ||||
−0.00481423 | + | 0.999988i | \(0.501532\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 11.8981i | − 0.644318i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 6.22637i | − 0.334249i | −0.985936 | − | 0.167125i | \(-0.946552\pi\) | ||||
0.985936 | − | 0.167125i | \(-0.0534482\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 17.4414i | − 0.933616i | −0.884359 | − | 0.466808i | \(-0.845404\pi\) | ||||
0.884359 | − | 0.466808i | \(-0.154596\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 8.70218i | − 0.463170i | −0.972815 | − | 0.231585i | \(-0.925609\pi\) | ||||
0.972815 | − | 0.231585i | \(-0.0743912\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 40.5871 | 2.15414 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.764263i | 0.0403362i | 0.999797 | + | 0.0201681i | \(0.00642015\pi\) | ||||
−0.999797 | + | 0.0201681i | \(0.993580\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 35.0886 | 1.84677 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.8648 | −1.09211 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.5162 | 1.38413 | 0.692067 | − | 0.721833i | \(-0.256700\pi\) | ||||
0.692067 | + | 0.721833i | \(0.256700\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.1310 | −1.04235 | −0.521173 | − | 0.853451i | \(-0.674505\pi\) | ||||
−0.521173 | + | 0.853451i | \(0.674505\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.25790i | 0.167790i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 10.2608i | − 0.527061i | −0.964651 | − | 0.263531i | \(-0.915113\pi\) | ||||
0.964651 | − | 0.263531i | \(-0.0848870\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.34315 | 0.119729 | 0.0598646 | − | 0.998207i | \(-0.480933\pi\) | ||||
0.0598646 | + | 0.998207i | \(0.480933\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.0440 | −1.21908 | −0.609540 | − | 0.792755i | \(-0.708646\pi\) | ||||
−0.609540 | + | 0.792755i | \(0.708646\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.0690 | −1.26780 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −25.0555 | −1.26068 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.3526i | 0.921088i | 0.887637 | + | 0.460544i | \(0.152346\pi\) | ||||
−0.887637 | + | 0.460544i | \(0.847654\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.96972 | 0.148301 | 0.0741503 | − | 0.997247i | \(-0.476376\pi\) | ||||
0.0741503 | + | 0.997247i | \(0.476376\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 25.5016i | − 1.27033i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.4418i | 0.517580i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.9502i | 1.18426i | 0.805842 | + | 0.592131i | \(0.201713\pi\) | ||||
−0.805842 | + | 0.592131i | \(0.798287\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.5319i | 1.40058i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.3065 | 1.77369 | 0.886844 | − | 0.462069i | \(-0.152893\pi\) | ||||
0.886844 | + | 0.462069i | \(0.152893\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.6274 | −1.10279 | −0.551396 | − | 0.834243i | \(-0.685905\pi\) | ||||
−0.551396 | + | 0.834243i | \(0.685905\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 36.8689i | − 1.78841i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.6040i | 1.47414i | 0.675816 | + | 0.737071i | \(0.263792\pi\) | ||||
−0.675816 | + | 0.737071i | \(0.736208\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 14.4650i | − 0.695146i | −0.937653 | − | 0.347573i | \(-0.887006\pi\) | ||||
0.937653 | − | 0.347573i | \(-0.112994\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 26.6802i | − 1.27629i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.10981 | −0.434788 | −0.217394 | − | 0.976084i | \(-0.569756\pi\) | ||||
−0.217394 | + | 0.976084i | \(0.569756\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 2.83319i | − 0.134609i | −0.997732 | − | 0.0673045i | \(-0.978560\pi\) | ||||
0.997732 | − | 0.0673045i | \(-0.0214399\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −40.5542 | −1.92245 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.3630 | −0.489058 | −0.244529 | − | 0.969642i | \(-0.578633\pi\) | ||||
−0.244529 | + | 0.969642i | \(0.578633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.13899 | 0.0536331 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.65951 | −0.311519 | −0.155759 | − | 0.987795i | \(-0.549782\pi\) | ||||
−0.155759 | + | 0.987795i | \(0.549782\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.71311i | 0.0797873i | 0.999204 | + | 0.0398936i | \(0.0127019\pi\) | ||||
−0.999204 | + | 0.0398936i | \(0.987298\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 24.1733i | − 1.12343i | −0.827331 | − | 0.561715i | \(-0.810142\pi\) | ||||
0.827331 | − | 0.561715i | \(-0.189858\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −37.2654 | −1.72444 | −0.862220 | − | 0.506535i | \(-0.830926\pi\) | ||||
−0.862220 | + | 0.506535i | \(0.830926\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.59436 | −0.303209 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 39.2385 | 1.80038 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.8596 | −0.998790 | −0.499395 | − | 0.866374i | \(-0.666444\pi\) | ||||
−0.499395 | + | 0.866374i | \(0.666444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.3803i | 1.02045i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 44.6259 | 2.02636 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 3.37269i | − 0.152831i | −0.997076 | − | 0.0764155i | \(-0.975652\pi\) | ||||
0.997076 | − | 0.0764155i | \(-0.0243475\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.68824i | 0.437224i | 0.975812 | + | 0.218612i | \(0.0701529\pi\) | ||||
−0.975812 | + | 0.218612i | \(0.929847\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.68332i | 0.346039i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 13.7401i | − 0.615089i | −0.951534 | − | 0.307545i | \(-0.900493\pi\) | ||||
0.951534 | − | 0.307545i | \(-0.0995074\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.92715 | 0.0859273 | 0.0429637 | − | 0.999077i | \(-0.486320\pi\) | ||||
0.0429637 | + | 0.999077i | \(0.486320\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.33316 | 0.237322 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 14.1621i | − 0.627723i | −0.949469 | − | 0.313862i | \(-0.898377\pi\) | ||||
0.949469 | − | 0.313862i | \(-0.101623\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 4.20473i | − 0.185283i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.03795i | 0.177589i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.6026i | 0.946427i | 0.880948 | + | 0.473213i | \(0.156906\pi\) | ||||
−0.880948 | + | 0.473213i | \(0.843094\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.9650 | 0.610648 | 0.305324 | − | 0.952249i | \(-0.401235\pi\) | ||||
0.305324 | + | 0.952249i | \(0.401235\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 60.1423i | − 2.61984i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.83952 | 0.427805 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.44125 | 0.105742 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.9928 | −0.994064 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.88005 | 0.166816 | 0.0834081 | − | 0.996515i | \(-0.473419\pi\) | ||||
0.0834081 | + | 0.996515i | \(0.473419\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 48.3652i | − 2.07174i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.1640i | 1.50351i | 0.659445 | + | 0.751753i | \(0.270791\pi\) | ||||
−0.659445 | + | 0.751753i | \(0.729209\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.17712 | −0.348357 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −42.4346 | −1.79801 | −0.899006 | − | 0.437936i | \(-0.855710\pi\) | ||||
−0.899006 | + | 0.437936i | \(0.855710\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.1339 | −0.597802 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.5488 | 0.697447 | 0.348724 | − | 0.937226i | \(-0.386615\pi\) | ||||
0.348724 | + | 0.937226i | \(0.386615\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 49.6790i | 2.09001i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.2566 | 1.01689 | 0.508446 | − | 0.861094i | \(-0.330220\pi\) | ||||
0.508446 | + | 0.861094i | \(0.330220\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 4.62563i | − 0.193576i | −0.995305 | − | 0.0967882i | \(-0.969143\pi\) | ||||
0.995305 | − | 0.0967882i | \(-0.0308569\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 19.3551i | − 0.807163i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.7907i | 1.11531i | 0.830072 | + | 0.557656i | \(0.188299\pi\) | ||||
−0.830072 | + | 0.557656i | \(0.811701\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.25850i | 0.259200i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.8591 | −1.14987 | −0.574933 | − | 0.818200i | \(-0.694972\pi\) | ||||
−0.574933 | + | 0.818200i | \(0.694972\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 64.0075 | 2.63738 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.56906i | 0.0644334i | 0.999481 | + | 0.0322167i | \(0.0102567\pi\) | ||||
−0.999481 | + | 0.0322167i | \(0.989743\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 40.1156i | − 1.63908i | −0.573021 | − | 0.819540i | \(-0.694229\pi\) | ||||
0.573021 | − | 0.819540i | \(-0.305771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.7827i | 1.01091i | 0.862854 | + | 0.505453i | \(0.168675\pi\) | ||||
−0.862854 | + | 0.505453i | \(0.831325\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.3550i | 1.19345i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.66240 | −0.189241 | −0.0946205 | − | 0.995513i | \(-0.530164\pi\) | ||||
−0.0946205 | + | 0.995513i | \(0.530164\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.65470i | 0.350132i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.5817 | 1.15440 | 0.577202 | − | 0.816601i | \(-0.304144\pi\) | ||||
0.577202 | + | 0.816601i | \(0.304144\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.1524 | −0.408720 | −0.204360 | − | 0.978896i | \(-0.565511\pi\) | ||||
−0.204360 | + | 0.978896i | \(0.565511\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.64022 | −0.347280 | −0.173640 | − | 0.984809i | \(-0.555553\pi\) | ||||
−0.173640 | + | 0.984809i | \(0.555553\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.2111 | −0.928442 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 52.7809i | 2.10451i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 5.46211i | − 0.217443i | −0.994072 | − | 0.108722i | \(-0.965324\pi\) | ||||
0.994072 | − | 0.108722i | \(-0.0346757\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.95947 | −0.276178 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.42822 | −0.0564114 | −0.0282057 | − | 0.999602i | \(-0.508979\pi\) | ||||
−0.0282057 | + | 0.999602i | \(0.508979\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.6036 | −0.970270 | −0.485135 | − | 0.874439i | \(-0.661229\pi\) | ||||
−0.485135 | + | 0.874439i | \(0.661229\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.2785 | −0.797229 | −0.398614 | − | 0.917119i | \(-0.630509\pi\) | ||||
−0.398614 | + | 0.917119i | \(0.630509\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 19.2740i | − 0.756570i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −42.8841 | −1.67818 | −0.839092 | − | 0.543990i | \(-0.816913\pi\) | ||||
−0.839092 | + | 0.543990i | \(0.816913\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 16.0060i | − 0.625407i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.4717i | 1.22596i | 0.790098 | + | 0.612981i | \(0.210030\pi\) | ||||
−0.790098 | + | 0.612981i | \(0.789970\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.3154i | 0.479015i | 0.970895 | + | 0.239507i | \(0.0769859\pi\) | ||||
−0.970895 | + | 0.239507i | \(0.923014\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.03351i | 0.156178i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.1226 | 0.583801 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.1864 | 1.43343 | 0.716716 | − | 0.697365i | \(-0.245645\pi\) | ||||
0.716716 | + | 0.697365i | \(0.245645\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.6046i | 1.36840i | 0.729296 | + | 0.684198i | \(0.239848\pi\) | ||||
−0.729296 | + | 0.684198i | \(0.760152\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.2056i | 1.23231i | 0.787623 | + | 0.616157i | \(0.211311\pi\) | ||||
−0.787623 | + | 0.616157i | \(0.788689\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.8622i | 0.453230i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.4141i | 0.511035i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.6168 | −1.46905 | −0.734527 | − | 0.678580i | \(-0.762596\pi\) | ||||
−0.734527 | + | 0.678580i | \(0.762596\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 38.7637i | 1.47039i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.75736 | 0.218076 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.8725 | −1.16604 | −0.583018 | − | 0.812459i | \(-0.698128\pi\) | ||||
−0.583018 | + | 0.812459i | \(0.698128\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −56.1730 | −2.11861 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.8452 | 1.49642 | 0.748209 | − | 0.663463i | \(-0.230914\pi\) | ||||
0.748209 | + | 0.663463i | \(0.230914\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 31.5729i | − 1.18241i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 12.8781i | − 0.481613i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.09266 | −0.0780431 | −0.0390216 | − | 0.999238i | \(-0.512424\pi\) | ||||
−0.0390216 | + | 0.999238i | \(0.512424\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.93207 | −0.220312 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.5164 | 0.798001 | 0.399000 | − | 0.916951i | \(-0.369357\pi\) | ||||
0.399000 | + | 0.916951i | \(0.369357\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −33.3330 | −1.23287 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 7.72856i | − 0.285461i | −0.989762 | − | 0.142730i | \(-0.954412\pi\) | ||||
0.989762 | − | 0.142730i | \(-0.0455882\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.6163 | 0.612070 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 16.1063i | − 0.592481i | −0.955113 | − | 0.296240i | \(-0.904267\pi\) | ||||
0.955113 | − | 0.296240i | \(-0.0957329\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.3296i | 1.07600i | 0.842945 | + | 0.537999i | \(0.180820\pi\) | ||||
−0.842945 | + | 0.537999i | \(0.819180\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 10.6174i | − 0.388993i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.5991i | 0.496238i | 0.968730 | + | 0.248119i | \(0.0798125\pi\) | ||||
−0.968730 | + | 0.248119i | \(0.920188\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −60.9252 | −2.21730 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.59688 | −0.0943851 | −0.0471926 | − | 0.998886i | \(-0.515027\pi\) | ||||
−0.0471926 | + | 0.998886i | \(0.515027\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 17.2920i | − 0.626833i | −0.949616 | − | 0.313416i | \(-0.898526\pi\) | ||||
0.949616 | − | 0.313416i | \(-0.101474\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 41.3106i | − 1.49164i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 41.4025i | − 1.49301i | −0.665378 | − | 0.746507i | \(-0.731730\pi\) | ||||
0.665378 | − | 0.746507i | \(-0.268270\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 29.4669i | − 1.05985i | −0.848044 | − | 0.529925i | \(-0.822220\pi\) | ||||
0.848044 | − | 0.529925i | \(-0.177780\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 46.4341 | 1.66796 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.12738i | 0.219536i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.2594 | 0.617591 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.84976 | 0.101712 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −54.1841 | −1.93146 | −0.965728 | − | 0.259557i | \(-0.916423\pi\) | ||||
−0.965728 | + | 0.259557i | \(0.916423\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.4128 | 1.15101 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 0.512549i | − 0.0181554i | −0.999959 | − | 0.00907771i | \(-0.997110\pi\) | ||||
0.999959 | − | 0.00907771i | \(-0.00288956\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.4110i | 0.722088i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.87261 | −0.313108 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 53.1407 | 1.86833 | 0.934164 | − | 0.356844i | \(-0.116147\pi\) | ||||
0.934164 | + | 0.356844i | \(0.116147\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.8127 | 0.379687 | 0.189843 | − | 0.981814i | \(-0.439202\pi\) | ||||
0.189843 | + | 0.981814i | \(0.439202\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 62.2196 | 2.17946 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 35.4753i | − 1.24112i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.70078 | 0.0942579 | 0.0471290 | − | 0.998889i | \(-0.484993\pi\) | ||||
0.0471290 | + | 0.998889i | \(0.484993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.6132i | 0.439670i | 0.975537 | + | 0.219835i | \(0.0705519\pi\) | ||||
−0.975537 | + | 0.219835i | \(0.929448\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 2.95803i | − 0.102861i | −0.998677 | − | 0.0514304i | \(-0.983622\pi\) | ||||
0.998677 | − | 0.0514304i | \(-0.0163780\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 15.8101i | − 0.549106i | −0.961572 | − | 0.274553i | \(-0.911470\pi\) | ||||
0.961572 | − | 0.274553i | \(-0.0885300\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 81.9324i | 2.83539i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.13130 | −0.177152 | −0.0885761 | − | 0.996069i | \(-0.528232\pi\) | ||||
−0.0885761 | + | 0.996069i | \(0.528232\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7638 | −0.957372 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.1911i | 0.488187i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.7084i | 0.949831i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.1627i | 1.54634i | 0.634198 | + | 0.773170i | \(0.281330\pi\) | ||||
−0.634198 | + | 0.773170i | \(0.718670\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.47725i | 0.0504618i | 0.999682 | + | 0.0252309i | \(0.00803210\pi\) | ||||
−0.999682 | + | 0.0252309i | \(0.991968\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.08183 | 0.105151 | 0.0525753 | − | 0.998617i | \(-0.483257\pi\) | ||||
0.0525753 | + | 0.998617i | \(0.483257\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.4000i | 1.57948i | 0.613445 | + | 0.789738i | \(0.289783\pi\) | ||||
−0.613445 | + | 0.789738i | \(0.710217\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −69.7381 | −2.37117 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.6547 | −0.361436 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.6144 | 1.20675 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.4774 | −1.70450 | −0.852251 | − | 0.523133i | \(-0.824763\pi\) | ||||
−0.852251 | + | 0.523133i | \(0.824763\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.66920i | 0.123619i | 0.998088 | + | 0.0618093i | \(0.0196870\pi\) | ||||
−0.998088 | + | 0.0618093i | \(0.980313\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.0393i | 0.607071i | 0.952820 | + | 0.303535i | \(0.0981671\pi\) | ||||
−0.952820 | + | 0.303535i | \(0.901833\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.8996 | 0.433126 | 0.216563 | − | 0.976269i | \(-0.430515\pi\) | ||||
0.216563 | + | 0.976269i | \(0.430515\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.7227 | −0.726924 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39.4863 | −1.31988 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.67667 | −0.322735 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.6353i | 1.05392i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.82299 | 0.293286 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.765170i | 0.0254071i | 0.999919 | + | 0.0127035i | \(0.00404377\pi\) | ||||
−0.999919 | + | 0.0127035i | \(0.995956\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 18.7415i | − 0.620934i | −0.950584 | − | 0.310467i | \(-0.899515\pi\) | ||||
0.950584 | − | 0.310467i | \(-0.100485\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.1330i | 0.401544i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.0460i | 0.694242i | 0.937820 | + | 0.347121i | \(0.112841\pi\) | ||||
−0.937820 | + | 0.347121i | \(0.887159\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.9928 | 1.21763 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.7506 | −1.33987 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 32.7286i | − 1.07379i | −0.843649 | − | 0.536895i | \(-0.819597\pi\) | ||||
0.843649 | − | 0.536895i | \(-0.180403\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 30.3713i | − 0.993246i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.53824i | 0.0829207i | 0.999140 | + | 0.0414603i | \(0.0132010\pi\) | ||||
−0.999140 | + | 0.0414603i | \(0.986799\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 46.1741i | − 1.50523i | −0.658459 | − | 0.752617i | \(-0.728791\pi\) | ||||
0.658459 | − | 0.752617i | \(-0.271209\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.02244 | 0.0984242 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.51338i | 0.0491782i | 0.999698 | + | 0.0245891i | \(0.00782775\pi\) | ||||
−0.999698 | + | 0.0245891i | \(0.992172\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.0170 | −0.617318 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.1132 | 1.39657 | 0.698287 | − | 0.715818i | \(-0.253946\pi\) | ||||
0.698287 | + | 0.715818i | \(0.253946\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 73.5741 | 2.38080 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44.7454 | 1.44340 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 46.9894i | 1.51264i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.5218i | 0.724253i | 0.932129 | + | 0.362127i | \(0.117949\pi\) | ||||
−0.932129 | + | 0.362127i | \(0.882051\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.4894 | 0.785902 | 0.392951 | − | 0.919559i | \(-0.371454\pi\) | ||||
0.392951 | + | 0.919559i | \(0.371454\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.6382 | −0.532302 | −0.266151 | − | 0.963931i | \(-0.585752\pi\) | ||||
−0.266151 | + | 0.963931i | \(0.585752\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.2454 | −0.551166 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.35617 | −0.170835 | −0.0854177 | − | 0.996345i | \(-0.527222\pi\) | ||||
−0.0854177 | + | 0.996345i | \(0.527222\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 78.9021i | − 2.51403i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.4988 | −0.556430 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.67605i | 0.148540i | 0.997238 | + | 0.0742698i | \(0.0236626\pi\) | ||||
−0.997238 | + | 0.0742698i | \(0.976337\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 19.4389i | − 0.616255i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.906930i | 0.0287228i | 0.999897 | + | 0.0143614i | \(0.00457153\pi\) | ||||
−0.999897 | + | 0.0143614i | \(0.995428\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7056.2.b.w.1567.7 | 8 | ||
3.2 | odd | 2 | 2352.2.b.l.1567.2 | yes | 8 | ||
4.3 | odd | 2 | 7056.2.b.x.1567.7 | 8 | |||
7.6 | odd | 2 | 7056.2.b.x.1567.2 | 8 | |||
12.11 | even | 2 | 2352.2.b.k.1567.2 | ✓ | 8 | ||
21.2 | odd | 6 | 2352.2.bl.o.31.1 | 8 | |||
21.5 | even | 6 | 2352.2.bl.r.31.4 | 8 | |||
21.11 | odd | 6 | 2352.2.bl.q.607.4 | 8 | |||
21.17 | even | 6 | 2352.2.bl.t.607.1 | 8 | |||
21.20 | even | 2 | 2352.2.b.k.1567.7 | yes | 8 | ||
28.27 | even | 2 | inner | 7056.2.b.w.1567.2 | 8 | ||
84.11 | even | 6 | 2352.2.bl.r.607.4 | 8 | |||
84.23 | even | 6 | 2352.2.bl.t.31.1 | 8 | |||
84.47 | odd | 6 | 2352.2.bl.q.31.4 | 8 | |||
84.59 | odd | 6 | 2352.2.bl.o.607.1 | 8 | |||
84.83 | odd | 2 | 2352.2.b.l.1567.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2352.2.b.k.1567.2 | ✓ | 8 | 12.11 | even | 2 | ||
2352.2.b.k.1567.7 | yes | 8 | 21.20 | even | 2 | ||
2352.2.b.l.1567.2 | yes | 8 | 3.2 | odd | 2 | ||
2352.2.b.l.1567.7 | yes | 8 | 84.83 | odd | 2 | ||
2352.2.bl.o.31.1 | 8 | 21.2 | odd | 6 | |||
2352.2.bl.o.607.1 | 8 | 84.59 | odd | 6 | |||
2352.2.bl.q.31.4 | 8 | 84.47 | odd | 6 | |||
2352.2.bl.q.607.4 | 8 | 21.11 | odd | 6 | |||
2352.2.bl.r.31.4 | 8 | 21.5 | even | 6 | |||
2352.2.bl.r.607.4 | 8 | 84.11 | even | 6 | |||
2352.2.bl.t.31.1 | 8 | 84.23 | even | 6 | |||
2352.2.bl.t.607.1 | 8 | 21.17 | even | 6 | |||
7056.2.b.w.1567.2 | 8 | 28.27 | even | 2 | inner | ||
7056.2.b.w.1567.7 | 8 | 1.1 | even | 1 | trivial | ||
7056.2.b.x.1567.2 | 8 | 7.6 | odd | 2 | |||
7056.2.b.x.1567.7 | 8 | 4.3 | odd | 2 |